X-ray diffraction investigation of the hexagonal-fcc structural transition in yttrium trihydride under hydrostatic pressure

Pressure induced structural transition of yttrium hydride has been investigated using synchrotron radiation X-ray diffraction measurement up to 24 GPa at room temperature. A reversible hexagonal-fcc transition with a wide intermediate region from 11 to 20 GPa is confirmed, which is consistent with previously reported X-ray results. The diffraction patterns measured for the intermediate state are not interpreted in terms of a hexagonal-fcc coexisting state or as rare-earth structures with various metal-layer stacking sequences. The equation of state determined for the hexagonal-YH₃ provides a bulk modulus B₀ of 71.9 GPa, which is nearly half of the previously reported value, but is within the range of values reported for other rare-earth metal trihydrides with hexagonal structures.     

An analogue oft-Designs in the association schemes of alternating bilinear forms

The notion of designs in an association scheme is defined algebraically by Delsarte [4]. It is known that his definition of designs has a geometric interpretation for known (P andQ)-polynomial association schemes except three examples. In this paper we give a geometric interpretation of designs in an association scheme of alternating bilinear forms, which is one of the three.     

On perfectt-shift codes in abelian groups

LetG be a finite abelian group,t a positive integer. Thet-shift sphere with centerx G is the setS _t (x)={±ix|i=1,...,t}. At-shift code is a subsetX ofG such that the setsS _t (x) (x X) have size 2t and are disjoint. Clearly, the sphere packing bound: 2t|X|+1|G| holds for anyt-shift codeX. Aperfect t-shift code is at-shift codeX with 2t|X|+1=|G|. A necessary and sufficient condition for the existence of a perfectt-shift code in a finite abelian group is known fort-1, 2. In this paper, we determine finite abelian groups in which there exists a perfectt-shift code fort=3, 4.This research was completed during the author's visit at the Institute for System Analysis, Moscow, as a Heizaemon Honda fellow of the Japan Association for Mathematical Sciences.     

New sterols from two edible mushrooms, Pleurotus eryngii and Panellus serotinus

Two edible mushrooms, Pleurotus eryngii and Panellus serotinus, have been investigated chemically. Two new sterols, 5alpha,9alpha-epidioxy-8alpha,14alpha-epoxy-(22E)-ergosta-6,22-dien-3beta-ol (1) and 3beta,5alpha-dihydroxyergost-7-en-6-one (2), have been isolated from P. eryngii, together with six known ones (3-8). Compound 1 was also isolated from P. serotinus. The structures of the new compounds were elucidated on the basis of their spectral data.     

Spontaneous copolymerization of 1,3-cycloheptadiene with acrylonitrile in the presence of zinc chloride

The reaction of 1,3-cycloheptadiene (1,3-CHpD) with acrylonitrile (AN) in the presence of ZnCl₂ leads spontaneously to the simultaneous formation of an alternating copolymer and a small amount of cycloadduct. The copolymer has a predominantly cis-1,4-structure. The formation of the charge—transfer complex between 1,3-CHpD and (AN)c (AN coordinated to ZnCl₂) in AN was detected by ultraviolet (UV) spectroscopy. The activation energies for the cycloaddition and for the copolymerization under the conditions used were determined to be 17.6 (in the presence of 1,1-diphenyl-2-picrylhydrazyl) and 16.3 kcal/mole, respectively. The rate of copolymerization in AN was found to depend on the 1.5th power of the concentrations of (AN)c and of 1,3-CHpD. Oxygen and UV irradiation causes an acceleration of the copolymerization only. On the basis of these results the mechanism of the spontaneous copolymerization is discussed and its relation to the cycloaddition in systems of 1,3-cyclodienes and AN in the presence of ZnCl₂ is mentioned.     

Sterol constituents from two edible mushrooms, Lentinula edodes and Tricholoma matsutake

Two new sterols, (22E)-23-methylergosta-5,7,22-trien-beta-ol (1) and 5alpha,6alpha-epoxy-(22E)-ergosta-8,14,22-triene -3beta,7alpha-diol (2), have been isolated from two edible mushrooms, Lentinula edodes and Tricholoma matsutake, respectively, together with twelve known ones (3-14). The structures of the new compounds were elucidated on the basis of their spectral data.